I Entangled particles in the thermal interpretation

Ah. It was skepticism about publishing, not about giving a comprehensive account!

Yes, I am preparing a book on quantum mechanics, which will contain an account of the thermal interpretation - but primarily to macroscopic, nonrelativistic reality, where it is obvious that it gives the correct view. And as a byproduct there will be a paper on the thermal interpretation alone.

Mainly I'm interested in how to "solve" the EPR paradox, which is why I quoted that post.

The proper treatment of the relativistic case (nonlocality problems begin only there!) needs relativistic quantum field theory, and hence is not subject of the book and the paper. In relativistic quantum field theory, there is no particle notion except asymptotically (at times ##\pm\infty##). Extended locality, as explained in the post you quoted, follows (with some handwaving) from the hyperbolic character of quantum field theory without any need for a particle interpretation. Thus it is valid independent of particles, and (as I showed in the context of that quote) is consistent with EPR.

I am still researching how precisely the nonrelativistic particle concept appears as an approximation of the relativistic situation; this is by no means trivial. It is clear that the approximations made are the real source of the difficulties with EPR, since EPR cannot even be formulated in QFT.

Until I understand this better, I cannot say much about entangled particles, except that they form an extended object as long as they are shielded from decoherence by careful arrangement of the environment.

Why can't they be formulated in QFT? I was looking for "Bell type experiment done in QFT", but I only found theorems on Bell's inequality violation of the vacuum. Is there a specific reason you cannot or is it just incredibly difficult?

In QFT (of the process including the source and the detector) one has a quantum system with an indefinite number of indistinguishable photons (including an unbounded number of soft photons), and there is no way to label within the QFT formalism two of these photons as being prepared or measured. I don't even know a publication doing this approximately in a reasonably convincing way. One can only consider the limit at infinite past or future times, where QFT simplifies to calculations in a Fock space. This gives scattering amplitudes but not the kind of information one needs to describe Bell-type experiments in finite time.

The standard techniques in high quality quantum optics simply work with free QED for the photons and a semiclassical few level approximation of single electrons in the detector, and model everything else in an approximation where one treats photons as ordinary quantum mechanical particles in the interaction picture (which doesn't exist in QFT by Haag's theorem), with suitable dissipation added to account for the open nature of the system. Simplified accounts at the level of the discussions here on PF even drop the dissipative terms and are then surprised about the counterintuitive results.

My own thoughts about this problem seem to indicate that the modeling of finite-time photons can be done approximately in QFT, but so far I have neither worked out the details nor the consequences for Bell-type experiments. It is a highly nontrivial problem.